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I have a simple question (I hope I can explain it clear enough). I want to train and apply a PCA to a set of data (I want to have an orthogonal basis in a low dimension subspace with unitary vectors), but the criteria that I want to maximize for the projected axes is not the variance of the data.

I was wondering if using the eigenvectors of a symmetric matrix other than the covariance matrix still gives a correct and usable basis.

For example: Let's say I have a symmetric matrix that represents a certain distance on each dimension computed over my data. Does the first eigen-vector of that matrix represent an axis that maximizes that distance ? And could the whole set of eigenvectors be used as basis ?

Sorry if the question is silly, but any response will be of big help. Thanks !

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    $\begingroup$ I don't quite understand. If you don't want to maximize the variance, what is it exactly that you're trying to do? Is it a form of multidimensional scaling? $\endgroup$ – Dougal Sep 5 '15 at 5:46
  • $\begingroup$ The question is not silly, only it is stingily asked. Explain by a concrete example. $\endgroup$ – ttnphns Sep 5 '15 at 10:17
  • $\begingroup$ @Dougal That was exactly what I was looking for, thanks !! $\endgroup$ – vphenix Sep 5 '15 at 12:09

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